1. Field of the Invention
The present invention relates to a method of producing a single crystal of a composition M3NbGa3Si2O14 useful as a piezoelectric material and a piezoelectric element made using the same.
2. Description of the Related Art
Up until now, the only reports regarding a single crystal of the composition M3NbGa3Si2O14 (where M in the composition is an alkaline earth metal) having a Ca3Ga2Ge4O14 structure (space group P321) have been findings on powder X-ray diffraction and structural analysis of Ca3NbGa3Si2O14 in Japanese Unexamined Patent Publication (Kokai) No. 11-171696 and the report of B. V. Mill et al. (Zh. Neorg. Khim., 1998, vol. 43, no. 8). There have not been any reports on growth of large, good quality single crystals.
Attempts have however been made to grow a single crystal by the Czochralski method (CZ method) of dipping a seed crystal in a melt in a crucible, pulling it up while rotating it, and thereby growing a single crystal at the lower end of the seed crystal for numerous compositions having a Ca3Ga2Ge4O14 structure.
When trying to grow either Ca3NbGa3Si2O14 or Sr3NbGa3Si2O14 using a seed crystal of a [001] orientation as found in many examples of growth of other compositions, as shown in FIG. 1 and FIG. 2, polycrystallization occurred immediately after the start of growth and a good single crystal could not be obtained.
An object of the present invention is to provide a method of producing a single crystal of a composition M3NbGa3Si2O14 (where M is an alkaline earth metal) having sufficient quality as a piezoelectric material and a piezoelectric element made using the same.
The present inventors engaged in in-depth studies on in what crystal orientation the crystal should be grown in order to achieve the object of the present invention taking into consideration the fact that a single crystal having a lattice direction identical to the lattice direction of the seed crystal used for pullup grows at the lower end of the seed crystal, for example, the Czochralski method, and as a result discovered that by growing the crystal in an orientation inclined by a predetermined angle from the [001] axis, more specifically by pulling up the crystal while bringing the melt into contact with the face inclined by a predetermined angle from the [001] axis of the seed crystal, a single crystal of a specific composition having sufficient quality as a piezoelectric material can be obtained and thereby completed the present invention.
According to a first aspect of the present invention, there is provided a method of producing a single crystal of a composition M3NbGa3Si2O14 (where M is an alkaline earth metal) comprising growing the crystal in a lattice direction inclined by an angle of 50.8 to 90 degrees from a [001] axis, preferably 51.4 to 90 degrees, particularly preferably 90 degrees. The closer the angle of inclination from the [001] axis to 90 degrees, the greater the size of the single crystal and the better the productivity of the single crystal.
According to a second aspect of the present invention, there is provided a method of producing a single crystal comprising pulling a seed crystal up while bringing a face, inclined at an angle of 50.8 to 90 degrees from a [001] axis of the seed crystal, into contact with a melt in a crucible, so that a single crystal of a composition M3NbGa3Si2O14 (where M is an alkaline earth metal) is grown at a lower end of the seed crystal.
The first and second aspects of the invention preferably the single crystal is grown at an angle ("psgr") of an enlarged crystal part of the crystal so as to satisfy the following formula when a pullup direction of the single crystal of said composition is made a direction xe2x80x9cvxe2x80x9d rotated by xcfx86 (50.8xe2x89xa6xcfx86xe2x89xa690) from the [001] axis in a plane including the [001] axis toward a vector xe2x80x9cva1xe2x80x9d extending in a direction vertical to the [001] axis and rotated xcex8 (0xe2x89xa6xcex8xe2x89xa630) from a [100] axis, xe2x80x9caxe2x80x9d and xe2x80x9ccxe2x80x9d are lattice constants, and "psgr" is an angle of the enlarged crystal part:
"psgr"xe2x89xa62 cosxe2x88x921((2 sin xcfx86cos xcex8/a+cos xcfx86/c)/((2/a)2+(1/c)2)xc2xd)
In the first and second aspects of the invention and their embodiments, preferably said alkaline earth metal is any one of Ca and Sr.
The first and second aspects of the invention preferably the crystal is grown at the angle of the enlarged crystal part of less than 78.4 degrees when pulling up the crystal in the [100] direction.
The first and second aspects of the invention preferably the crystal is grown at the angle of the enlarged crystal part of less than 95.6 degrees when pulling up the crystal in a [120] direction.
According to third aspect of the present invention, there is provided a seed crystal comprised of a composition M3NbGa3Si2O14 (where M is an alkaline earth metal) and having a face of which a crystal orientation inclined at an angle of 50.8 to 90 degrees from a [001] axis, preferably 51.4 to 90 degrees, particularly preferably 90 degrees.
According to fourth aspect of the present invention, there is provided a single crystal comprised of a composition M3NbGa3Si2O14 (where M is an alkaline earth metal) and having a face of which a crystal orientation inclined at an angle of 50.8 to 90 degrees from a [001] axis, preferably 51.4 to 90 degrees, particularly preferably 90 degrees.
The single crystal according to the present invention can be suitably used as a component of a resonator, filter, or other various types of piezoelectric elements.
According to fifth aspect of the present invention, there is provided a piezoelectric element comprised of a single crystal including a composition M3NbGa3Si2O14 (where M is an alkaline earth metal) and having a face of which a crystal orientation inclined at an angle of 50.8 to 90 degrees from a [001] axis, preferably 51.4 to 90 degrees, particularly preferably 90 degrees.
Note that in the present specification, the xe2x80x9cenlarged crystal partxe2x80x9d means the shoulder enlarged to a predetermined size in the single crystal grown at the lower end of the seed crystal (corresponding to reference numeral 30 in FIG. 6B). The angle of the enlarged crystal part is the angle of the enlarged crystal part with respect to the pullup direction (corresponding to 2xcfx89 in FIG. 6B).
Further, in the present invention, for example, when expressing the xe2x80x9c(hk1) planexe2x80x9d, this is indicated as xe2x80x9c(hk*1)xe2x80x9d.
Ca3NbGa3Si2O4 Composition
The single crystal having a Ca3Ga2Ge4O14 structure in previous reports on crystal growth, like the many oxide single crystals currently industrialized, are grown by pulling the crystals up by the Czochralski method in the [001] direction (=z-axis=c-axis, see FIG. 13). No problem of polycrystallization occurred so long as the temperature gradient at the time of growth was held in a suitable range. FIG. 13 is a schematic view for explaining the pullup direction of the crystal.
For a Ca3NbGa3Si2O14 composition, however, when actually growing a crystal by pulling it up in the [001] direction, as shown in FIG. 1, polycrystallization occurs immediately after the start of the growth, then a transparent crystal portion was obtained in a growth orientation vertical to the [120] direction (=y-axis, see FIG. 13) and inclined in the [100] direction (=x-axis =a1 axis, see FIG. 13). The obtained transparent crystal portion was cut out and used as a seed crystal for growth of a single crystal, whereupon, as shown in FIG. 3, a crystal having a twinning plane was obtained. FIG. 1 and FIG. 3 are both views of examples of growth of Ca3NbGa3Si2O14 by methods of the related art.
The twinning plane of the obtained crystal was examined in detail, whereupon it could be confirmed that the normal vector had an inclination of about 10 degrees with respect to the [100] direction from the [001] direction. The (21*0) plane (=x-plane) of the twinning plane was measured for lattice direction by a Laue camera, whereupon it could be confirmed that the regions at the two sides of the twinning plane were offset by about 20 degrees in the [001] direction. From these results, as the twinning plane, either the 116 ([001] direction and 11.6 degrees) and the 117 ([001] direction and 9.9 degrees) may be considered, but the 117 facet with a good match with the measured value was judged as the twinning plane.
Note that in the present specification, the plane described as xe2x80x9chk1xe2x80x9d, since {hk1} and {h*k*1} are deemed equivalent, expresses all of (hk1), (k(h+k)*1), ((h+k)*h1), (h(h+k)*1*), ((h+k)*k1*), (kh1*), (h*k*1), (k*(h+k)1), ((h+k)h*1), (h*(h+k)1*), ((h+k)k*1*), and (k*h*1*).
As shown in FIG. 4, however, in fact growth striations 20, 20 . . . such as shown in FIG. 5A and FIG. 5B were observed in the single crystal grown by pulling up the crystal in the [100] direction. If using the growth striations 20, 20 . . . as planes and reading the angle formed with the normal vector and [100] direction, the result becomes about 40 degrees (see FIG. 5A) and about 30 degrees (see FIG. 5B) and these become the (21*1) plane, the (21*1*) plane, the (100) plane, and the (11*0) plane. FIG. 4 is a view of an example of growth of Ca3NbGa3Si2O14 by the method of the related art, FIG. 5A schematically shows the growth striations of the Ca3NbGa3Si2O14 shown in FIG. 4 as seen from the [120] direction (=y-axis), and FIG. 5B is a left side view of FIG. 5A.
From the above results, the present inventors considered that they could avoid the problem of polycrystallization by suppressing growth of the 117 facet during crystal growth, considered that as a measure toward this, it would be effective to grow the crystal in a direction giving superior growth of the 111 facet corresponding to the growth striations 20 shown in FIG. 5, actually confirmed this, and thereby completed the present invention.
Note that the xe2x80x9cdirection of growth of the crystalxe2x80x9d spoken of here is not limited to the pullup direction in the Czochralski method and means any direction in which crystal actually grows in the process of crystal growth, that is, all directions vertical to the solid-liquid interface of the crystal growth interface.
As a method for suppressing polycrystallization, first, when the pullup direction of the single crystal is the [120] direction, as shown in FIG. 6B, it is sufficient to control the direction of growth of the single crystal by limiting it to an angle such that the (21*7) plane and (21*7*) plane, which are factors behind polycrystallization, do not appear. Specifically, it is sufficient to control the direction of growth of the single crystal by limiting it to the angle (xcfx89) formed between the normal vectors of the (21*1) plane adjoining the (21*7) plane and the (21*1*) plane adjoining the (21*7*) plane with the [100] direction. The angle xcfx89 in the present embodiment is less than 39.2 degrees, preferably not more than 38.6 degrees. Therefore, when the pullup direction of the crystal is the [100] direction, it is possible to effectively suppress polycrystallization by growing the crystal while controlling the angle ("psgr") of the enlarged crystal part 30 to less than 78.4 degrees (39.2 degreesxc3x972), preferably not more than 77.2 degrees (38.6 degreesxc3x972). Note that if "psgr" is less than 78.4 degrees, the value may be close to 0 degree (90 degreesxe2x88x9290 degrees). The smaller the "psgr" value, however, the smaller the diameter of the single crystal obtained, so the lower the production efficiency of the single crystal. Therefore, the "psgr" value is preferably as large as possible. When crystal was actually grown with an angle of the enlarged crystal part of 70 degrees, as shown in FIG. 7, it could be confirmed that the polycrystallization could be suppressed. FIG. 6A is a schematic view of a facet when pulling up Ca3NbGa3Si2O14 in the [100] direction, FIG. 6B is a schematic view of FIG. 6A seen from the [120] direction (=y-axis), and FIG. 7 is a view of an example of growth of Ca3NbGa3Si2O14 obtained by the method of the present invention.
From the above, when pulling up the crystal in a direction rotated from [001] axis toward [100] direction, it is sufficient to pull up the crystal using a seed crystal having a lattice direction inclined by an angle of at least 50.8 degrees (=90 degreesxe2x88x9239.2 degrees) from the [001] axis, preferably at least 51.4 degrees (=90 degreesxe2x88x9238.6 degrees). Note that the inclination from the [001] axis should be at least 50.8 degrees, particularly preferably 90 degrees (90 degreesxe2x88x920 degree). The closer the inclination from the [001] axis to 90 degrees, the larger the angle ("psgr") of the enlarged crystal part that can be obtained and as a result the better the production efficiency of the single crystal obtained.
Second, when the pullup direction of the single crystal is the [120] direction, as shown in FIG. 8 to FIG. 10, it is sufficient to control the direction of growth of the single crystal by limiting it to an angle such that the (117) plane, (1*27) plane, (117*) plane, and (1*27*) plane, which are factors behind polycrystallization, do not appear. Specifically, it is sufficient to control the direction of growth of the single crystal by limiting it to the angle (xcfx89) formed between the normal vectors of the (111) plane adjoining the (117) plane, the (1*21) plane adjoining the (1*27) plane, the (111*) plane adjoining the (117*) plane, and the (1*21*) plane adjoining the (1*27*) plane and the [120] direction. The angle xcfx89 in the present embodiment is less than 47.8 degrees, preferably not more than 47.4 degrees. Therefore, when the pullup direction of the crystal is the [120] direction, it is possible to suppress polycrystallization by growing the crystal while controlling the angle ("psgr") of the enlarged crystal part 30 to less than 95.6 degrees (47.8 degreesxc3x972), preferably not more than 94.8 degrees (47.4 degreesxc3x972). Note that if "psgr" is less than 95.6 degrees, the value may be close to 0 degree (90 degreesxe2x88x9290 degrees). The smaller the "psgr" value, however, the smaller the diameter of the single crystal obtained, so the lower the production efficiency of the single crystal. Therefore, the "psgr" value is preferably as large as possible. FIG. 8 is a schematic perspective view for explaining the crystal structure of Ca3NbGa3Si2O14 obtained by the method of the present invention, FIG. 9 is a schematic view of FIG. 8 seen from the [120] direction (=y-axis), and FIG. 10 is a sectional view along the Xxe2x80x94X line of FIG. 9 and shows the facet when pulling up the Ca3NbGa3Si2O14 in the [120] direction.
From the above, when pulling up the crystal in a direction rotated from [001] axis toward [120] direction, it is sufficient to pull up the crystal using a seed crystal having a lattice direction inclined by an angle of at least 42.2 degrees (=90 degreesxe2x88x9247.8 degrees) from the [001] axis, preferably at least 42.6 degrees (=90 degreesxe2x88x9247.4 degrees). Note that the inclination from the [001] axis should be at least 42.2 degrees, particularly preferably 90 degrees (90 degreesxe2x88x920 degree). The closer the inclination from the [001] axis to 90 degrees, the larger the angle ("psgr") of the enlarged crystal part that can be obtained and as a result the better the production efficiency of the single crystal obtained.
Third, when the pullup direction of the crystal is between the [100] direction and the [120] direction, not including the [001] direction, the smallest angle formed with the pullup direction during the growth of the 111 facet suppressing growth of the 117 facet is the angle ("psgr") of 39.2 degrees formed between the normal vectors of the (21*1) plane and (21*1*) plane at the time of pullup in the [100] direction and the [100] direction. Therefore, when the pullup direction of the crystal does not include the [001] direction, by growing the crystal while controlling the angle ("psgr") of the enlarged crystal part to less than 78.4 degrees (39.2 degreesxc3x972), preferably not more than 77.2 degrees (38.6 degreesxc3x972), it is possible to effectively suppress polycrystallization. Note that if "psgr" is less than 78.4 degrees, it may be a value close to 0 degree (90 degreesxe2x88x9290 degrees), but the smaller than "psgr" value, the smaller the size of the single crystal and as a result the lower the production efficiency of the single crystal, so the "psgr" value preferably is as large as possible.
Due to the above, when pulling up the crystal in a direction not including the [001] direction, it is sufficient to pull up the crystal using a seed crystal having a lattice direction inclined by an angle of at least 50.8 degrees (=90 degreesxe2x88x9239.2 degrees) from the [001] axis, preferably at least 51.4 degrees (=90 degreesxe2x88x9238.6 degrees). Note that the inclination from the [001] axis should be at least 50.8 degrees, particularly preferably 90 degrees (90 degreesxe2x88x920 degree). The closer the inclination from the [001] axis to 90 degrees, the larger than angle ("psgr") of the enlarged crystal part that can be taken and as a result the more improved the productivity of the single crystal obtained.
The angle "psgr" of the enlarged crystal part can be controlled for example by the temperature at the time of growth, the pullup speed, the output of the radio frequency generator, the output of the heater, etc.
Sr3NbGa3Si2O14 Composition
A crystal of the composition Sr3NbGa3Si2O14 was grown by pulling it up in the [001] direction, whereupon, as shown in FIG. 2, polycrystallization was observed immediately after the start of growth. FIG. 2 is a view of an example of growth of Sr3NbGa3Si2O14 obtained by the method of the related art.
Therefore, when growing a crystal at a pullup direction consisting of a direction inclined about 60 degrees from the [001] axis, as shown in FIG. 11, it was not possible to grow a perfect single crystal, but by pulling up the crystal in the [100] direction, as shown in FIG. 12, a transparent, crack free single crystal could be obtained. FIG. 11 is a view of an example of growth of Sr3NbGa3Si2O14, while FIG. 12 is a view of an example of growth of Sr3NbGa3Si2O14 obtained by the method of the present invention.
Due to the above, when growing a single crystal shown by the composition M3NbGa3Si2O14 (wherein M is an alkaline earth metal), the pullup direction of the crystal, in other words, the lattice direction of the seed crystal used, is important. Further, when desiring to grow such a single crystal with good productivity, the angle of the enlarged crystal part is important.
Relations
In the following explanation, general formulas will be found for the relations between the pullup direction of the crystal and the angle of enlargement at the shoulder (corresponding to reference numeral 30 in FIG. 6B).
First, a single crystal having a Ca3NbGa3Si2O14 structure belongs to the space group P321, so the c-axis is three-fold symmetry axis and the a-axis is a two-fold symmetry axis. Therefore, when the inclination from the a-axis exceed the xc2x130 degree range in the plane vertical to the c-axis, the inclination from the a-axis becomes equivalent to the xc2x130 degree range due to the three-fold symmetry axis of the c-axis.
Here, the vector v (xcex8,xcfx86) of the pullup direction of the crystal pulled up in the present invention, as shown in FIG. 13, is made a direction rotated xcfx86 degrees from the [001] axis in the plane including the [001] axis toward the vector va extending in the direction vertical to the [001] axis and rotated by xcex8 degrees (xe2x88x9230xe2x89xa6xcex8xe2x89xa630) from the [100] axis. Due to the two-fold symmetry at the a-axis, the vector v (xcex8,xcfx86) becomes equivalent to the vector v (xe2x88x92xcex8,180xe2x88x92xcfx86). Note that in the present invention, the (117) plane and the (1*1*7) plane are equivalent, so the vector v (xcex8,xcfx86) is deemed as equivalent to the vector v (xe2x88x92xcex8,xcfx86). Therefore, the vector showing the pullup of the single crystal may be considered to be in the range of only 0xe2x89xa6xcex8xe2x89xa630 and 0xe2x89xa6xcfx86xe2x89xa690.
When growing the single crystal in the pullup direction, that is, 0xe2x89xa6xcex8xe2x89xa630, 0xe2x89xa6xcfx86xe2x89xa690, the 117 facet of the smallest angle with the pullup direction becomes the (21*7) plane, while the 111 facet suppressing facet growth in that direction becomes the (21*1) plane. Therefore, the angle of the enlarged crystal part enabling growth of the single crystal of the above composition has to be no more than "psgr" shown by the formula ("psgr"=2xcfx89). Note that the angle xcfx89 is the angle formed by the normal vector of the (21*1) plane and the pullup direction v.
Further, the normal vector in the (hk1) plane is expressed, by the xyz coordinate system, as (h/a, (2k+h)/a3, 1/c), SO the normal vector of the (21*1*) plane becomes (2/a, 0, 1/c).
Further, the orientation V (xcex8,xcfx86)(=pullup direction) rotated xcfx86 degrees in the va vector direction from the c-axis in the plane vertical to the c-axis (=z-axis) and including the vector va rotated xcex8 degrees from the al axis (=x-axis) and c-axis is shown by v=(sin xcfx86 cos xcex8, sin xcfx86 sin xcex8, cos xcex8).
Since xcfx89 is equal to the angle formed by the vector v and the (21*1) normal vector, xcfx89 becomes cosxe2x88x921((2 sin xcfx86 cos xcex8/a+cos xcfx86/c)/((2/a)2+(1/c)2)xc2xd). Therefore, "psgr" becomes 2 cosxe2x88x921((2 sin xcfx86 cos xcex8/a+cos xcfx86/c)/((2/a)2+(1/c)2)xc2xd).
Further, when pulling up a Ca3NbGa3Si2O14 single crystal (lattice constant a =8.112 xc3x85, c=5.078 xc3x85) with respect to the a1 axial direction (=x-direction), since xcex8=0 and xcfx86=90, the angle of the enlarged crystal part becomes not more than 77.2 degrees. Further, when pulling it up in the y-direction, since xcex8=30 and xcfx86 =90, the angle of the enlarged crystal parte becomes not more than 94.8 degrees. Further, the normal vector of the (211) plane becomes (0.2465, 0, 0.1969) and xcfx86 is calculated as 51.38 degrees (xcfx89=0 degree), so in the case of a Ca3NbGa3Si2O14 single crystal, xcfx86 becomes the range of 51.38xe2x89xa6xcfx86xe2x89xa690.
Similarly, when pulling up a Sr3NbGa3Si2O14 single crystal (lattice constant a=8.284 xc3x85, c=5.080 xc3x85) with respect to the a1 axial direction (=x-direction), since xcex8=0 and xcfx86=90, the angle of the enlarged crystal part becomes not more than 78.4 degrees. Further, when pulling it up in the y-direction, since xcex8=30 and xcfx86=90, the angle of the enlarged crystal part becomes not more than 95.68 degrees. Further, the normal vector of the (21*1) plane becomes (0.2414, 0, 0.1969) and xcfx86 is calculated as 50.80 degrees (xcfx89=0 degree), so in the case of a Sr3NbGa3Si2O14 single crystal, xcfx86 becomes the range of 50.8xe2x89xa6xcfx86xe2x89xa690.
Therefore, the relationship between the pullup orientation v of the single crystal of the composition M3NbGa3Si2O14 (where M is an alkaline earth metal) and the angle "psgr" of the enlarged part of the crystal can be expressed by "psgr"=2 cosxe2x88x921 ((2sin xcfx86cos xcex8/a+cos xcfx86/c)/((2/a)2+(1/c)2)xc2xd). Provided, however, that the xcex8 in the formula is 0xe2x89xa6xcex8xe2x89xa630 and xcfx86 is 50.8xe2x89xa6xcfx86xe2x89xa690.
The present disclosure relates to subject matter contained in Japanese Patent Application No. 2000-150245, filed on May 22, 2000, the disclosure of which is expressly incorporated herein by reference in its entirety.